Boundary Value Problems For A Differential Equation On A Measure Chain
نویسنده
چکیده
We will prove existence and uniqueness theorems for solution of the boundary value problem x∆∆(t) = f(t, xσ(t)), x(a) = A, x(σ2(b)) = B for t in a measure chain T. In one of our results we use upper and lower solutions to prove the existence of a solution to this boundary value problem (BVP). We then use this result to show that if for each fixed t, f(t, x) is strictly increasing in x, then this BVP has a unique solution. In our last result we get an existence-uniqueness theorem in the case where f satisfies a one sided Lipschitz condition.
منابع مشابه
Studies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
Abstract. The Sturm-Liouville boundary value problem of the multi-order fractional differential equation is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.
متن کاملStudies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
...
متن کاملExistence of solutions of boundary value problems for Caputo fractional differential equations on time scales
In this paper, we study the boundary-value problem of fractional order dynamic equations on time scales, $$ ^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin [0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1
متن کاملExistence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
متن کاملF-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM
We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...
متن کاملL2-transforms for boundary value problems
In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.
متن کامل